Gumbel Plot
Produces a Gumbel plot, a diagnostic plot for checking whether the data appears to be from a Gumbel distribution.
guplot(object, ...)
guplot.default(y, main = "Gumbel Plot",
xlab = "Reduced data", ylab = "Observed data", type = "p", ...)
guplot.vlm(object, ...)y |
A numerical vector. |
main |
Character. Overall title for the plot. |
xlab |
Character. Title for the x axis. |
ylab |
Character. Title for the y axis. |
type |
Type of plot. The default means points are plotted. |
object |
An object that inherits class |
... |
Graphical argument passed into
|
If Y has a Gumbel distribution then plotting the sorted values y_i versus the reduced values r_i should appear linear. The reduced values are given by
r_i = - log(- log(p_i))
where p_i is the ith plotting position, taken here to be (i-0.5)/n. Here, n is the number of observations. Curvature upwards/downwards may indicate a Frechet/Weibull distribution, respectively. Outliers may also be detected using this plot.
The function guplot is generic, and
guplot.default and guplot.vlm are some
methods functions for Gumbel plots.
A list is returned invisibly with the following components.
x |
The reduced data. |
y |
The sorted y data. |
The Gumbel distribution is a special case of the GEV distribution with shape parameter equal to zero.
T. W. Yee
Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.
Gumbel, E. J. (1958). Statistics of Extremes. New York, USA: Columbia University Press.
## Not run: guplot(rnorm(500), las = 1) -> ii names(ii) guplot(with(venice, r1), col = "blue") # Venice sea levels data ## End(Not run)
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